EduSahara™ Worksheet

Question 1

1.

A chord that passes through the centre of the circle is called

(i)

radius
(ii)

major segment
(iii)

semi-circle
(iv)

diameter
(v)

circumference

Question 2

2.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

major segment
(ii)

radius
(iii)

circumference
(iv)

segment
(v)

diameter

Question 3

3.

The segment of the circle containing the centre of the circle is called

(i)

major segment
(ii)

semi-circle
(iii)

centre
(iv)

chord
(v)

radius

Question 4

4.

Which of the following statements are true?

a)	Every circle has a unique diameter.
b)	Every circle has a unique centre.
c)	Each radius of a circle is also a chord of the circle.
d)	A line can meet a circle atmost at two points.
e)	A circle consists of an infinite number of points.

(i)

{c,d}
(ii)

{a,b,d}
(iii)

{b,d,e}
(iv)

{a,b}
(v)

{a,c,e}

Question 5

5.

Which of the following statements are true?

a)	Two semi-circles of a circle together make the whole circle.
b)	An infinite number of chords may be drawn for a circle.
c)	An infinite number of diameters may be drawn for a circle.
d)	Every circle has a unique diameter.
e)	One and only one tangent can be drawn to a circle from a point outside it.

(i)

{d,a}
(ii)

{a,b,c}
(iii)

{d,a,b}
(iv)

{d,e,c}
(v)

{e,b}

Question 6

6.

In the given triangle S is the circumcentre. If SE = 11.80 cm, find the circumference of the circumcircle

(i)

72.2 cm
(ii)

76.2 cm
(iii)

75.2 cm
(iv)

73.2 cm
(v)

74.2 cm

Question 7

7.

Find the side of the square in the following figure if the radius of the circle is 13.00 cm.

(i)

20.38 cm
(ii)

18.38 cm
(iii)

16.38 cm
(iv)

17.38 cm
(v)

19.38 cm

Question 8

8.

If a chord EF = 16 cm is drawn in a circle with radius OE = 11 cm, find its distance from the centre of the circle

(i)

6.55 cm
(ii)

7.55 cm
(iii)

9.55 cm
(iv)

5.55 cm
(v)

8.55 cm

Question 9

9.

The diameter GH of a circle with centre 'O' is perpendicular to the chord EF. If EF = 22.00 cm and GI = 7.08 cm, find the radius of the circle.

(i)

10.08 cm
(ii)

14.08 cm
(iii)

13.08 cm
(iv)

11.08 cm
(v)

12.08 cm

Question 10

10.

'B' and 'C' are centres of circles of radii 2 cm and 9 cm such that BC = 17 cm and 'D' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠BDC = 90°, find 'r'

(i)

8 cm
(ii)

4 cm
(iii)

5 cm
(iv)

7 cm
(v)

6 cm

Question 11

11.

Which of the following statements are true?

a)	Atmost one chord can be drawn on a circle with a certain length.
b)	The diameter is the longest chord.
c)	The radius is the shortest chord.
d)	A chord divides a circle into two sectors.
e)	A chord divides a circle into two segments.

(i)

{c,e}
(ii)

{d,a,b}
(iii)

{b,e}
(iv)

{a,b}
(v)

{c,e,b}

Question 12

12.

Which of the following statements are true?

a)	Equal length chords subtend equal angles at the centre of the circle.
b)	No two chords bisects each other.
c)	The longest chord of the circle passes through the centre of the circle.
d)	Equal length chords are equidistant from the centre of the circle.
e)	The farther the chord is from the centre, the larger the angle it subtends at the centre.

(i)

{a,c,d}
(ii)

{b,e,d}
(iii)

{b,a,c}
(iv)

{e,c}
(v)

{b,a}

Question 13

13.

Which of the following statements are true?

a)	The diameter divides the circle into two unequal parts.
b)	The area enclosed by a chord and its major arc is called major segment.
c)	A sector is the area enclosed by two radii and a chord.
d)	The area enclosed by a chord and its minor arc is called minor segment.
e)	A circle divides the plane on which it lies into three parts.

(i)

{a,b,d}
(ii)

{a,b}
(iii)

{b,d,e}
(iv)

{a,c,e}
(v)

{c,d}

Question 14

14.

Which of the following statements are true?

a)	The midpoint of any diameter of a circle is its centre.
b)	The diameter divides the circle into two unequal parts.
c)	The longest of all chords of a circle is called diameter.
d)	A sector is the area enclosed by two radii and a chord.
e)	Two chords bisect each other.

(i)

{e,b,a}
(ii)

{d,c,a}
(iii)

{d,c}
(iv)

{b,a}
(v)

{a,c}

Question 15

15.

Which of the following statements are true?

a)	A radius is a limiting case of a diameter.
b)	A secant and a chord are same.
c)	A tangent is the limiting case of a secant.
d)	A diameter is a limiting case of a chord.
e)	A secant has two end points.

(i)

{b,d}
(ii)

{b,d,c}
(iii)

{a,c}
(iv)

{c,d}
(v)

{e,a,c}

Question 16

16.

DE , FG , HI , JK are chords of a circle with DE = 5 cm , FG = 1 cm , HI = 6.7 cm and JK = 7.04 cm. The chord farthest from the centre of the circle is

(i)

FG = 1 cm
(ii)

DE = 5 cm
(iii)

HI = 6.7 cm
(iv)

JK = 7.04 cm

Question 17

17.

In the given figure, A and B are centres of two circles with equal radii intersecting at C and D. If AB = 20 cm and CD = 14.8 cm, find the radii of the circles

(i)

10.44 cm
(ii)

13.44 cm
(iii)

14.44 cm
(iv)

12.44 cm
(v)

11.44 cm

Question 18

18.

In the given figure, two circles of radii EG = 15.4 cm & FG = 8 cm intersect at G & H. The distance between the centres EF = 20 cm, find the length of GH

(i)

10.29 cm
(ii)

13.29 cm
(iii)

12.29 cm
(iv)

11.29 cm
(v)

9.29 cm

Question 19

19.

In the given figure, O is the centre of the circle. J is a point on chord HI such that HJ = JI. Find ∠OJH

(i)

105°
(ii)

100°
(iii)

120°
(iv)

90°
(v)

95°

Question 20

20.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 6 cm